Here, we considered minimally-coupled test scalar perturbations on exact BH and wormhole solutions of scalar-tensor theory, which possess an effective negative cosmological constant, leading to AdS asymptotics, due to the presence of a non-minimally coupled `gravitational' scalar to the Einstein tensor. We find that similar effects arise in the late-time ringdown waveform for both compact objects under study. After the initial ringdown, the test field response exhibits echoes, with timescales proportional to the non-minimal coupling constant. Although the BH considered here does not contain any quantum corrections at the event horizon, the effective asymptotic AdS boundary, that the gravitational scalar introduces to the scalarized solution, forces the partially reflected waves from the PS to mirror off the AdS boundary and re-perturb the PS to give rise to a damped beating pattern which is strikingly similar to echoes from quantum corrected compact objects [1]}. The existence of echoes in such AdS-like BHs may lead to interesting interpretations of such a phenomenon on dual holographic descriptions at the boundary, as AdS/CFT suggests (see [2]}, [3]} for a holographic description of echoes on a dual CFT at the near-horizon quantum structure).
